Generation of two correlated stationary Gaussian processes and application to ship rolling motion

Abstract

A model of series expansion with random amplitudes is proposed to generate two correlated Gaussian stochastic processes. The spectral density of each process can be adjusted to fit that of any practical process, and the correlation coefficient of the two processes can be specified arbitrarily. The model is then used to simulate two correlated random ocean wave forces of Pierson–Moskowitz spectrum. Based on the model, ship rolling motion under two correlated wave forces is investigated. The focus is on the effect of the correlation of the two random wave forces. Two different situations are considered. When the wave forces are weak, capsizing will not occur, and the motion will reach the stationary state after a period of time. The stationary probability densities of the rolling angle are calculated by simulation. It is found that the effect of the correlation on the long-term behavior of the ship rolling motion may be neglected. Another situation is with strong wave forces, in which case capsizing may happen as a random event. The ship rolling motion is non-stationary transient process before capsizing occurs. The average capsizing time is calculated also by simulation. It is shown that the correlation may have significant effect on the capsizing process, depending on system and excitation parameters.